3.4 Introduction to Matrices:
This branch of mathematics
is useful in the study of Science, Engineering, Economics and other fields.
The 11 railway connections
between cities of Karnataka, Maharashtra and
No 
Starting
place 
Destination 
1 
Mangaluru 
Mumbai 
2 
Mangaluru 
Pune 
3 
Hubballi 
Pune 
4 
Belagavi 
Nagapura 
5 
Mumbai 

6 
Mumbai 

7 
Pune 

8 
Pune 

9 
Pune 
Vadodara 
10 
Nagapura 

11 
Nagapura 
Vadodara 
Can you tell quickly the
number of direct connection between Mangaluru and
We will solve this problem
in chapter 3.6
Let us read the following
paragraph.
On Monday the attendance in
your class was 30 girls and 22 boys and seven were absent. On Tuesday the
attendance was 28 girls and 26 boys and 5 were absent. On Wednesday the attendance
was 26 boys and 27 girls and six were absent. Thursday was a republic day and
there were no classes. On Friday the attendance was 30 boys and 23 girls and
six were absent. On Saturday the attendance was 34 boys and 24 girls and one
was absent.
From the above data can you
easily answer following questions?
1. Which day had maximum
attendance?
2. Which day had maximum
absentees?
3. On which day girls’
attendance was more than boys?
4. For how many days was
girls’ attendance more than boys?
Since the data was in
narration form, it was not that easy to answer these questions. Let us
represent the data in a tabular form as shown below:
A= _{}
In this
representation 1. The
numbers in six horizontal rows represent attendance details for a week from
Monday to Saturday. 2. The
numbers in the first vertical column represent the attendance of girls for
six days. 3. The
numbers in the second vertical column represent the attendance of boys for
six days. 4. The
numbers in the third vertical column represent the number of absentees for
six days. With
the above representation, we can easily answer the questions: 1.
Saturday had maximum attendance (only one student was absent) 2.
Monday had maximum absentees (7) 3.
Monday had maximum attendance of girls 4. On
three days (Monday, Tuesday and Wednesday) attendance of girls was more than
that of boys 

Definition : A ‘matrix’
is a rectangular representation of data in rows and columns, normally enclosed within brackets.
Definitions: Each number or entity in a matrix is called ‘element’ The
horizontal representations are called ‘rows’. The
vertical representations are called ‘columns’. In the
Attendance example discussed above, Matrix A has 6 rows and 3 columns. It is called a 6 by
3 (6X3) matrix. The order of a matrix is denoted by (m x n),
where m is number of rows and n is number of columns in the matrix. 

In the
adjacent Matrix B, the four sets of row elements are(p1,p2,p3),(q1,q2,q3),(r1,r2,r3)
and(s1,s2,s3). The
three sets of column elements are (p1,q1,r1,s1),(p2,q2,r2,s2)
and(p3,q3,r3,s3). Thus
matrix B has 4 rows and 3 columns and hence is a 4 by
3 (4X3) Matrix. 
B= _{} 
3.4
Summary of learning
No 
Points
studied 
1 
Definition
of matrix, rows, columns, order 